Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Good just isn't Good enough. Best System Probabilities and the Foundations of Statistical Mechanics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two strategies, viz. a globalist as suggested by Loewer, and a localist as advocated by Frigg and Hoefer. Both strategies fail because the system they are part of have rivals that are roughly equally good, while ontic probabilities should be part of a clearly winning system. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Schulpraktika in der Lehrerbildung. Theoretische Grundlagen, Konzeptionen, Prozesse und Effekte = Pedagogical field experiences in teacher education. Theoretical foundations, programmes, processes, and effects

Seit mehr als zwanzig Jahren werden in der tertiären Lehramtsausbildung Schulpraktika reformiert und neuerdings in ihrem zeitlichen Umfang relativ zur Studienzeit vergrößert. Zum Gegenstand reger Forschungsaktivitäten avancierten Schulpraktika jedoch erst im letzten Jahrzehnt. Hiermit werden ein Überblick über das Forschungsfeld (Grundlagen der schulpraktischen Komponenten der Lehrerbildung; Forschungsmethodik) vorgelegt und aktuelle Forschungsergebnisse zu zentralen Aspekten der Wirksamkeit von Praktika und Effekten von Mentoring präsentiert. In englischsprachigen bzw. deutschsprachigen Beiträgen wird der Forschungsstand in Deutschland, den Niederlanden, Österreich und der Schweiz sowie den USA aufgezeigt. Der Band richtet sich an Personen, die in der Lehrerbildung tätig sind, also an Dozent/inn/en in Hochschulen und Seminaren, an Lehrerbildungsforscher/innen sowie an Fachpersonen in der Bildungsadministration und interessierte Studierende.

Three essays on the concept of trust and its foundations

The present dissertation focuses on trust and comprises three empirical essays on the concept itself and its foundations. All three essays investigate trust as an expectation and rely on selfreport measures of trust. Whereas the first two chapters investigate social trust, the third chapter investigates political trust. Essentially, there are three related important debates to which the following chapters contribute. A first debate discusses problems with current selfreport measures. Scholars recently started to question whether standard trust questions really measure the same across countries and languages. Chapter 1 engages in this debate. Using data from Switzerland it studies whether different trust questions measure the same latent trust constructs across individuals belonging to three different culturallinguistic regions. The second debate concerns the socalled forms or dimensions of trust. Recently, scholars started investigating whether trust is a onedimensional construct, i.e. whether an individual's trust judgment differs for categories of trustees such as strangers, neighbors, family members and friends or not. Relying on confirmatory factor analysis Chapter 2 investigates whether individuals really do make a difference between different trustee categories and to what extent these judgments can be summarized into higherorder latent trust constructs. The third debate is concerned with causes of differences in trust across humans. Chapter 3 focuses on the role of laterlife experiences, more precisely victimization experiences and investigates their causal relationship with generalized social trust. Chapter 4 focuses on the impact of direct democratic institutions on the trust relationship between citizens and political authorities.

Searching the hearts of graphene-like molecules for simplicity, sensitivity and logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.

Probabilistic Justification Logic

We present a probabilistic justification logic, PPJ, to study rational belief, degrees of belief and justifications. We establish soundness and completeness for PPJ and show that its satisfiability problem is decidable. In the last part we use PPJ to provide a solution to the lottery paradox.